How does one prove comprehension in machines?
This is one of the most important issues in the philosophy of artificial intelligence. 

The most famous philosophical argument that attempts to address this issue is the Chinese Room argument published by the philosopher John Searle in 1980. 

The argument is quite simple. Suppose that you are inside a room and you need to communicate (in a written form) with people outside the room in a certain language that you do not understand (in the particular example given by Searle, Chinese), but you are given the rules to manipulate the characters of this language (for a given input, you have the rules to produce the correct output). If you follow these rules, to the people outside the room, it will seem as if you understand this language, but you don't. 

To be more concrete, when I say "apple", you understand that it refers to a specific fruit because you have eaten apples and you have a model of the world. That's understanding, according to Searle.

The most famous mathematical model of computers, the Turing machine, is essentially a system that manipulates symbols, so the Chinese Room argument directly applies to computers. 

Many replies or counterarguments to the CR argument have been discussed, such as


the system reply (the symbol manipulator is only a part of the larger system).
the robot reply (the symbol manipulator does not understand the meaning of the symbols because it has not experienced the associated real-world objects, so it suggests that understanding requires a body with sensors and controllers)
the brain simulator reply (the symbol manipulator can actually simulate the activity in the brain of a person that understands the unknown language)


So, can we prove that machines really understand? Even before Searle, Turing had already asked the question "Can machines think?". To prove this, you need a rigorous definition of understanding and thinking that people agree on. However, many people do not want to agree on a definition of intelligence and understanding (hence the many counterarguments to the CR argument). So, if you want to prove that machines understand, you need to provide a proof with respect to a specific definition of understanding. For example, if you think that understanding is just a side effect of symbol manipulation, you can easily prove that machines understand many concepts (it just follows from the definition of a Turing machine). However, even if understanding was just a side effect (what does a side effect actually mean in this case?) of symbol manipulation, would a machine be able to understand the same concepts and in the same way that humans understand? It's harder to answer this question because we really do not know if humans only manipulate symbols in our brains.